Question 1 (15 marks) A swimmer nds that her times (x, measured in minutes) for swimming 3 SO-meter distance follow a normal distribution: x~N(3.2,02). She trained intensively for It) days and got her swimming times: 4.7, 2.9, 3.1, 3.5, 2.8, 3.4, 3.6, 2.7. 3.5, 3.2 After training, she wants to know whether her mean swimming time has been changed. (a) Work out the sample mean and sample standard deviation of the swimming time. [2] (b) Set up H" and H,. [2] (c) Suggest. with remnant), a suitable statistical test to test the hypotheses set in part (b). [3] (d) Assume that a = 5%, determine the critical value and. hence, the rejection regionts). [2] (c) Work out the value of the test statistic. [3] (f) Test if there is any evidence that the swimming times has been changed. State the decision and draw conclusion clearly. [3]